# Modelling microwave cavities for dielectric measurement

**Speaker:** John Blackburn

**Title:** Modelling microwave cavities for dielectric measurement

**Abstract:** This talk describes over 10 years of effort in modelling microwave cavities (dielectric resonators) at

the National Physical Laboratory. The idea is to put a device under test into a cavity and measure the resonance frequency and Q-factor. By predicting theoretically what these should be for a given sample, we can work backwards and predict the permittivity and loss of the device under test. There are many different techniques for modelling cavities all of which reduce to eigenvalue problems. I will discuss two techniques: finite difference and mode matching. The latter, which is less well known, is a quasi analytical technique in which known Maxwell solutions for parts of the cavity are stitched together to form an eigenproblem with a very small matrix (no meshing is needed but the geometry must be simple). The downside is that forming this matrix requires the solution of an internal eigenvalue problem giving a “double eigenvalue” system which can be tricky. I will discuss various cavities and compare TE, TM and hybrid modes which must be treated in different ways.